login
a(n) = floor(e*(n-1)*(n-1)!).
4

%I #44 Sep 06 2023 22:34:24

%S 0,2,10,48,260,1630,11742,95900,876808,8877690,98641010,1193556232,

%T 15624736140,220048367318,3317652307270,53319412081140,

%U 909984632851472,16436597430879730,313262209859119578,6282647653285676000,132266266384961600020,2916471173788403280462

%N a(n) = floor(e*(n-1)*(n-1)!).

%C Also the number of positive integers with all distinct digits expressed in base n. E.g., a(10) = Sum_{j=1..10} A073531(j). - _Labos Elemer_, Dec 05 2002

%C For example, for n=3 we have 1, 2, 10, 12, 20, 21, 102, 120, 201, 210 (10 numbers in total). - _Igor Krasikov_, Aug 14 2023

%F G.f.: Q(0)/(2*x) - 1/x - 1/(1-x), where Q(k) = 1 + 1/(1 - x*(k+1)/(x*(k+1) + (1-x)/Q(k+1) )); (continued fraction). - _Sergei N. Gladkovskii_, Aug 08 2013

%F a(n) = 2*(A038155(n) - A038155(n-1)). - _Anton Zakharov_, Oct 13 2016

%t Table[Apply[Plus, Table[((b-1)/b)*Binomial[b, j]*j!, {j, 1, b}]], {b, 1, 25}]

%Y Cf. A001113, A073531, A073532.

%Y a(n) = A001339(n)-1.

%Y Equals (n-1)*A000522(n-1).

%K nonn

%O 1,2

%A _N. J. A. Sloane_